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hegel_phenomenology_of_spirit_preface_part_4.mp3
38. Now because the system of spirit's experience embraces only the appearance of spirit, it seems to be the case that the advance from this system to the science of the true in the shape of the true is merely negative, and one might wish to be spared the negative (as the false) and demand instead to be taken without further ado straight to the truth. Why bother with the false at all? - What was mentioned above, namely, that perhaps we should have begun straight away with science, may be answered here by taking into consideration that aspect which has to do with the general make-up of the negative when it is regarded as the false. Ordinary ideas on this subject especially obstruct the entrance to the truth. This will provide an opportunity to speak about mathematical cognition, which non-philosophical knowledge looks upon as the ideal which philosophy must try to attain but towards which it has so far striven in vain.
39. The true and the false belong to those determinate thoughts that are regarded as motionless essences unto themselves, with one standing fixedly here and the other standing fixedly there, and each being isolated from the other and sharing no commonality. Against that view, it must be maintained that truth is not a stamped coin issued directly from the mint and ready for one's pocket. Nor is there "a" false, no more than there is "an" evil. To be sure, evil and falsehood are not as bad as the devil, since, if they are taken as the devil, they are made into particular subjects. However, as false and evil, they are only universals, even though they have an essentiality of their own vis-à-vis each other. - The false, for it is only the false which is being spoken of here, would be the other, the negative of substance which, as the content of knowledge, is the true. However, the substance is itself essentially the negative, in part as the distinction and the determination of the content, and in part as a simple act of distinguishing, which is to say, as the self and knowledge as such. To be sure, we can know falsely. For something to be known falsely means that knowledge is in disparity with its substance. Yet this very disparity is the act of distinguishing per se, the essential moment. It is indeed out of this distinction that its parity comes to be, and this parity, which has come to be, is truth. However, it is not truth in the sense that would just discard disparity, like discarding the slag from pure metal, nor even is it truth in the way that a finished vessel bears no trace of the instrument that shaped it. Rather, as the negative, disparity is still itself immediately on hand, just as the self in the true as such is itself on hand. For that reason, it cannot be said that the false constitutes a moment or even a constituent part of the true. Take the saying that "In every falsehood there is something true" - in this expression both of them are regarded as oil and water, which cannot mix and are merely externally combined. It is precisely for sake of pointing out the significance of the moment of complete otherness that their expression must no longer be employed in the instances where their otherness has been sublated. Just as the expressions, "unity of subject and object" or of "the finite and infinite," or of "being and thought," etc., have a certain type of clumsiness to them in that subject and object, etc., mean what they are outside of their unity, and therefore in their unity, they are not meant in the way their expression states them, so too the false as the false is no longer a moment of truth.
40. The dogmatism of the way of thinking, in both the knowledge of philosophy and the study of it, is nothing but the opinion that truth consists either in a proposition which is a fixed result or else in a proposition which is immediately known. To questions like, "When was Caesar born?", "How many toise were there in a stadion and what did they amount to?", etc., a neat and tidy answer is supposed to be given, just as it is likewise determinately true that the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right-angled triangle. However, the nature of such a so-called truth is different from the nature of philosophical truths.
41. With regard to historical truths, to take note of them very briefly, it is the case that insofar as they are examined in light of what is purely historical in them, it will be readily granted that they have to do with individual existence, with a contingent and arbitrary content, and with the non-necessary determinations of that individual existence. - However, even bare truths like those cited in the example do not exist without the movement of self-consciousness. In order to know any one of them, there has to be a good deal of comparison, books also have to be consulted, or, in some way or other, inquiry has to carried out. Even in the case of immediate intuition, acquaintance with them is held to be of true value only when such acquaintance is linked to the reasons behind it, even though it is really just the unadorned result itself which is supposed to be at issue.
42. As for mathematical truths, one would hardly count as a geometer if one only knew Euclid's theorems by heart without knowing the proofs, or, so it might be expressed by way of contrast, without knowing them really deep down in one's heart. Likewise, if by measuring many right-angled triangles, one came to know that their sides are related in the well-known way, the knowledge thus gained would be regarded as unsatisfactory. Nonetheless, the essentiality of the proof in the case of mathematical cognition does not yet have the significance and the nature of being a moment in the result itself; rather, in the result, the proof is over and done with and has vanished. As a result, the theorem is arguably one that is seen to be true. However, this added circumstance has nothing to do with its content but only with its relation to the subject. The movement of mathematical proof does not belong to the object but is an activity that is external to the item at hand. The nature of a right-angled triangle does not divide itself up in the manner exhibited in the mathematical construction which is necessary for the proof of the proposition expressing its ratio. The whole act of bringing the result to light is a process and a means of cognition. - In philosophical cognition, the coming-to-be of existence as existence is also different from the coming-to-be of essence, that is, the inner nature of the thing at issue. However, in the first place, philosophical cognition contains both, whereas in contrast mathematical cognition exhibits only the coming-to-be of existence, i.e., the coming-to-be of the being of the nature of the thing at issue in cognition as such. Moreover, philosophical cognition also unites these two particular movements. The inward emergence, or the coming-to-be, of substance is an undivided transition into the external, that is, into existence, into being for another, and conversely, the coming-to-be of existence is its taking-itself-back into essence. In that way, the movement is the twofold process and coming-to-be of the whole, so that at the same time each posits the other, and, for that reason, each in itself also has both of them as two viewpoints. Together they make the whole by dissolving themselves and making themselves into moments of the whole.
43. In mathematical cognition, insight is an external activity vis-à-vis the item at issue. It follows that the true item at issue is thereby altered. The tools, the construction and the proof thus do indeed contain true propositions. However, it must nonetheless be stated that the content is false. The triangle in the above example is taken apart, and its parts are then affixed onto other figures which the construction which is contained in the triangle permits to emerge. It is only at the end that the triangle which is really at issue is reinstated; it was lost to view during the course of the procedure and appeared only in fragments that belonged to other wholes. - Thus, we see here the negativity of the content making its entrance on to the scene, a negativity which would have to be called a falsity of the content just as much as, in the movement of the concept, one would have to speak of the disappearance of supposedly fixed thoughts.
44. But the genuine defectiveness of this kind of cognition has to do with cognition itself as much as it does with its material. - In the first place, as to what concerns cognition, no insight into the necessity of the construction is achieved. The necessity does not emerge from the concept of the theorem. Rather, it is imposed, and one is instructed to draw just these lines when an infinite number of others could have been drawn and to obey blindly the injunction without any more knowledge on one's part other than the fond belief that this will serve the purpose of leading to the proof. This purposiveness also turns out later on to be merely external because it is only afterwards, in the proof itself, that it first becomes evident. - Likewise, the proof itself takes a path that begins anywhere, without one knowing as yet what relation this beginning has to the result that is supposed to emerge. In the progress of the proof, it incorporates these determinations and relations and leaves others alone, but it does this without immediately seeing what necessity there is in the matter. It is an external purpose which controls this movement.
45. The convincingness of this defective cognition is something about which mathematics is proud and brags about to philosophy, but it rests solely on the poverty of its purpose and the defectiveness of its material, and it is for that reason the kind of thing that philosophy must spurn. - Its purpose, that is, its concept, is magnitude. It is precisely this relationship which is non-essential and devoid of the concept. For that reason, the movement of knowledge in mathematics takes place only on the surface; it does not touch on the thing that really matters, does not touch on the essence, that is, the concept, and hence it does not constitute any kind of comprehension of what is at stake. - The material that provides mathematics with this gratifying wealth of truths consists of space and numerical units. Space is the existence in which the concept inscribes its distinctions as it would in an empty, dead element in which the distinctions themselves are just as unmoved and lifeless. The actual is not something spatial as it is taken to be in mathematics; neither concrete sensuous intuition nor philosophy wastes any time with the kinds of non-actualities which are the things of mathematics. In such non-actual elements, there are then only non-actual truths, which is to say, fixed, dead propositions; one can call a halt to any of them, but the next begins anew on its own account without the first itself having moved on to another and without any necessary connection arising out of the nature of the thing at issue. - It is also on account of that principle and element - and what is formal in mathematical convincingness consists in this - that knowledge advances along the line of equality. Precisely because it does not move itself, what is lifeless does not make it all the way to the distinctions of essence, nor to essential opposition, that is, to disparity, nor to the transition of one opposition into its opposite, nor to qualitative, immanent self-movement. For it is magnitude alone, the inessential distinction, that mathematics deals with. It is the concept that divides space into its dimensions and determines the combinations and in space; mathematics abstracts from that. Mathematics does not consider, for example, the relation of line to surface, and when it compares the diameter of a circle with its circumference, it runs up against their incommensurability, which is to say, a ratio lying in the concept, that is, an infinite, which itself eludes mathematical determination.
46. Immanent, so-called pure mathematics also does not set time, as time, over and against space as the second material for its study. Applied mathematics, to be sure, deals with time in the way it deals with motion and other actual things, but it incorporates synthetic propositions, i.e., propositions about their ratios which are determined by their concept. It takes those synthetic propositions from experience, and it merely applies its formulae to those presuppositions. That the so-called proofs of such propositions which applied mathematics frequently provides, such as those concerning the equilibrium of the lever, the relation of space and time in falling motion, etc., should be given and accepted as proofs is itself only proof of how great the need for proof is for cognition, since even where it has no more proof, knowledge still respects the empty semblance of proof and even thereby attains a kind of satisfaction. A critique of those proofs would be as odd as it would be instructive; in part, it would cleanse mathematics of this kind of false polish, and in part it would point out both its limitations and thereby the necessity for another type of knowledge. - As for time: One might presume that time, as the counterpart to space, would constitute the material of the other division of pure mathematics, but time is the existing concept itself. The principle of magnitude, that is, the principle of the conceptless distinction, and the principle of equality, that is, that of abstract, lifeless unity, are incapable of dealing with that pure restlessness of life and its absolute distinction. Only as something paralyzed, namely, as the [quantitative] one, does this negativity thereby become the second material of this act of cognition, which, itself being an external activity, reduces what is self-moving to "stuff" simply in order now to have in that "stuff" an indifferent, external, lifeless content.
47. In contrast, philosophy does not study inessential determinations but only those that are essential. The abstract or the non-actual is not its element and content; rather, its element and content is the actual, what is self-positing, what is alive within itself, that is, existence in its concept. It is the process which creates its own moments and passes through them all; it is the whole movement that constitutes the positive and its truth. This movement equally includes within itself the negative, or what would be called "the false" if it were to be taken as something from which one might abstract. It is what disappears and which is to an even greater degree itself to be taken as essential, but not as having the determination of something fixed, something cut off from the truth, which along the way is to be set aside (who knows where?) as something that lies outside of the truth, just as the truth also cannot be thought of as what is lifelessly positive and completely at rest. Appearance is both an emergence and a passing away which does not itself emerge and pass away but which instead exists in itself and which constitutes the actuality and the living movement of truth. The truth is the bacchanalian revel where not a member is sober, because, in isolating himself from the revel, each member is just as immediately dissolved into it - the ecstasy is likewise transparently and simply motionless. Judged in the court of that movement, the individual shapes of spirit do not durably exist any more than do determinate thoughts, but they are also equally positive, necessary moments just as much as they are negative, disappearing moments. - In the whole of the movement, apprehended as being at rest, what distinguishes itself within it and what gives itself existence is preserved as what remembers, as that whose existence is its knowledge of itself, just as this self-knowledge is no less immediate existence.
48. It might seem necessary to state at the outset the principal points concerning the method of this movement, that is, the method of science. However, its concept lies in what has already been said, and its genuine exposition belongs to logic, or is to a greater degree even logic itself, for the method is nothing but the structure of the whole in its pure essentiality. However, on the basis of what has been said up until now, we must be aware that the system of representations relating to philosophical method itself also belongs to an already vanished cultural shape. - If this may perhaps sound somewhat boastful or revolutionary, even though I take myself to be far from striking such a tone, then it is still worthwhile to keep in mind that the scientific régime bequeathed by mathematics - a régime of explanations, classifications, axioms, a series of theorems along with their proofs, principles, and the consequences and inferences to be drawn from them - has in common opinion already come to be regarded as itself at the least out of date. Even though it has not been clearly seen just exactly why that régime is so unfit, little to no use at all is any longer made of it, and even though it is not condemned in itself, it is nonetheless not particularly well liked. And we must be prejudiced in favor of the excellent and believe that it can put itself to use and bring itself into favor. However, it is not difficult to see that the mode of setting forth a proposition, producing reasons for it, and then also refuting its opposite with an appeal to reasons is not the form in which truth can emerge. Truth is the movement of itself in itself, but the former method is that of a cognition which is external to its material. For that reason, such a method is peculiar to mathematics and must be left to mathematics, which, as noted, has for its principle the conceptless relationship of magnitude and takes its material from dead space as well as from the equally lifeless numerical unit. In a freer style, that is to say, in a mélange of even more quirks and contingency, it may also persist in ordinary life, say, in a conversation or in the kind of historical instruction which satisfies curiosity more than it results in knowledge, in the same way that, more or less, a preface does. In everyday life, consciousness has for its content little bits of knowledge, experiences, sensuous concretions, as well as thoughts, principles, and, in general, it has its content in whatever is on hand, or in what counts as a fixed, stable entity or essence. In part, consciousness continues on this path, and in part it interrupts the whole context by means of a free, arbitrary choice about such content in which it conducts itself as if it were an external act of determination and manipulation of that content. It leads the content back to some kind of certainty, even if it may be only the feeling of the moment, and its conviction is satisfied when it arrives at some familiar resting-place.
49. However, let it be granted that the necessity of the concept has banished the slipshod style of those conversations which are composed out of merely clever argumentation, and let it also be granted that it has also banished the inflexibility of scientific pomposity. It does not follow, as we have already noted, that its place ought be swapped for the "un- method" that bases itself on either vague sentiments or on inspiration, nor does it follow that it should be swapped for the capriciousness of prophetic chatter. Both of these approaches despise not merely the scientific rigor of the necessity of the concept; they despise scientific rigor altogether.
50. When triplicity was rediscovered by Kantian thought - rediscovered by instinct, since at that time the form was dead and deprived of the concept - and when it was then elevated to its absolute significance, the true form was set out in its true content, and the concept of science was thereby engendered - but there is almost no use in holding that the triadic form has any scientific rigor when, as we now see it, it has been reduced to a lifeless schema, to a mere façade, and when scientific organization itself has been reduced to a tabular chart.- We spoke earlier in wholly general terms about this formalism, but now we wish to state more precisely just what its approach is. This formalism takes itself to have comprehended and articulated the nature and life of a shape when it affirmed a determination of the schema to be a predicate of that life or shape. - The predicate may be subjectivity or objectivity, or it may be that of magnetism, electricity, or, for that matter, contraction or expansion, East or West, and so forth. All of them can be infinitely multiplied, since in this way of proceeding each determination or shape can be used as a form or moment of the schema for every other determination, and each moment can profitably perform the same service for the other - a circle of reciprocity whose result is that one neither learns from experience about the thing at issue nor does one learn what one or the other of the reciprocal elements is. In such a way of proceeding, what partly happens is that sensuous determinations are picked up out of ordinary intuition, determinations which of course are supposed to mean something different from what they say, and what partly happens is that the pure determinations of thought, that is, what is meaningful in itself, such as subject, object, substance, cause, the universal, etc., are each used as uncritically and unquestioningly as they are used in everyday life, indeed, in the same way that expressions like "strong" and "weak," and "expansion" and "contraction" are used. In the former case, the metaphysics is thereby as unscientific as are those sensuous representations in the latter case.
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